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<ADP wanted , pyramid , 2 spheres

Source: : V Soros Olympiad 1998-99 Round 3 11.10 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 26, 2024
geometry3D geometrypyramidsphere

Problem Statement

The plane angles at vertex DD of the pyramid ABCDABCD are equal to α\alpha,β\beta and γ\gamma (∠CDB=a\angle CDB = a). An arbitrary point MM is taken on edge CBCB. A ball is inscribed in each of the pyramids ABDMABDM and ACDMACDM. Let us draw through DD a plane distinct from BCDBCD, tangent to both balls and not intersecting the segment connecting the centers of the balls. Let this plane intersect the segment AMAM at point PP. What is ∠ADP\angle ADP equal to?
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